A finite element model for the nonlinear analysis of reinforced and prestressed masonry walls

A materially nonlinear layered finite element model is proposed for the analysis of reinforced and/or prestressed masonry wall panels under monotonie loadings in the plane and/or out of the plane, capable of evaluating both the serviceability load and the ultimate load. An orthotropic incrementally linear relationship and equivalent uniaxial concept are used to represent the behaviour of masonry under biaxial stresses while a uniaxial bilinear elasto-plastic model with hardening is employed for rebar and the so-called ‘power-formula’ is adopted to describe the stress-strain relationship of prestressing steel.

After cracking, the smeared coaxial rotating crack model is adopted and tension stiffening, reduction in compressive strength and stiffness after cracking, and strain softening in compression are accounted for. The modified Newton-Raphson iteration method is employed to ensure convergency of non linear solution.

The proposed finite element model has been tested by a comparison with experimental data available in literature, both for reinforced and prestressed wall panels. The analysis of results shows good agreement between the values obtained by the proposed model and those obtained experimentally.     

Nonlinear finite element analysis of concrete structures using new constitutive models

Nonlinear finite element analysis was applied to various types of reinforced concrete structures using a new set of constitutive models established in the fixed-angle softened-truss model (FA-STM). A computer code FEAPRC was developed specifically for application to reinforced concrete structures by modifying the general-purpose program FEAP. FEAPRC can take care of the four important characteristics of cracked reinforced concrete: (1) the softening effect of concrete in compression, (2) the tension-stiffening effect by concrete in tension, (3) the average (or smeared) stress–strain curve of steel bars embedded in concrete, and (4) the new, rational shear modulus of concrete. The predictions made by FEAPRC are in good agreement with the experimental results of beams, panels, and framed shear walls.     

Computer-aided analysis of reinforced concrete columns subjected to axial compression and bending. Part II: T-shaped sections

This paper presents the writer's experience in investigating numerically the strength behaviour of short T-shaped reinforced concrete (RC) columns in order to provide design aids for structural engineers. Computer programs were developed for the analytical study of T-shaped RC column sections subjected to uniaxial/biaxial bending with axial compression. The interaction curves for L-shaped members, in Part I [Mallikarjuna and P. Mahadevappa, Comput. Struct. 44, 1121–1138 (1992)], and for T-shaped sections, in the present paper, were derived to provide advice for design information. This paper deals with the definitions and materials that are used in the limit state design of reinforced concrete structures. The programs presented here are written to operate in a conversational mode so that the analyst can respond to messages from the computer.     

Non-linear finite element dynamic analysis of two-dimensional concrete structures

This paper presents a numerical procedure for predicting the non-linear dynamic response of plane and axisymmetric reinforced concrete structures. Isoparametric elements with special embedded axial members are used to discretize concrete and steel in space. A summary of a rate and history dependent constitutive model for progressive failure analysis of concrete is given in which the compression behaviour is modelled as a strain rate sensitive elasto-viscoplastic material and in tension as strain rate dependent linear elastic strain softening material. The different rales governing the pre-failure and post-failure behaviour in compression and tension are developed in which the strain rate dependency is included. Steel is modelled as a strain rate dependent uniaxial elasto-viscoplastic material. Explicit central difference scheme in conjunction with an energy balance check is employed for time integration of equations of motion. A computer program for linear and non-linear dynamic analysis of concrete structures is described. Finally, some numerical applications are presented.     

Design optimization of 3D reinforced concrete structures

This paper presents a computer-based method for the optimal design of three-dimensional reinforced concrete (RC) skeletal structures having members subjected to biaxial moments, biaxial shears and axial loads. The width, depth and area of longitudinal reinforcement of member sections are taken as the design variables. The optimality criteria (OC) method is applied to minimize the cost of the concrete, steel and formwork for the structure. The primary focus of the paper concerns fundamental issues related to the formulation of design performance constraints on combined axial load, biaxial moments and biaxial shears. An example problem is solved with and without account for biaxial shear constraints to illustrate their influence on the design.     

Analysis of cyclic loading of plane RC structures

A numerical procedure for cyclic loading response of planar reinforced concrete structures is presented. A nonlinear orthotropic stress strain law for biaxially loaded plain concrete is developed and compared with experimental results for monotonic biaxial loading and uniaxial cyclic loading. The stress-strain law recognizes strength and ductility changes due to biaxial stress, and strength and stiffness degradation with cycles of loading. The stress strain law is incorporated into a finite element computer program which utilizes isoparametric quadrilaterals with extra non-conforming deformation modes. Numerical and experimental results are presented for a monotonically loaded shear wall-frame system and a cyclically loaded shear wall.     

Nonlinear finite element analysis of reinforced concrete plates and shells under monotonic loading

Plane stress constitutive models are proposed for the nonlinear finite element analysis of reinforced concrete structures under monotonic loading. An elastic strain hardening plastic stress-strain relationship with a nonassociated flow rule is used to model concrete in the compression dominating region and an elastic brittle fracture behavior is assumed for concrete in the tension dominating area. After cracking takes place, the smeared cracked approach together with the rotating crack concept is employed. The steel is modeled by an idealized bilinear curve identical in tension and compressions. Via a layered approach, these material models are further extended to model the flexural behavior of reinforced concrete plates and shells. These material models have been tested against experimental data and good agreement has been obtained.     

A layered cylindrical quadrilateral shell element for nonlinear analysis of RC plate structures

This paper proposes a simple and accurate 4-node, 24-DOF layered quadrilateral flat plate/shell element, and an efficient nonlinear finite element analysis procedure, for the geometric and material nonlinear analysis of reinforced concrete cylindrical shell and slab structures. The model combines a 4-node quadrilateral membrane element with drilling or rotational degrees of freedom, and a refined nonconforming 4-node 12-DOF quadrilateral plate bending element RPQ4, so that displacement compatibility along the interelement boundary is satisfied in an average sense. The element modelling consists of a layered system of fully bonded concrete and equivalent smeared steel reinforcement layers, and coupled membrane and bending effects are included. The modelling accounts for geometric nonlinearity with large displacements (but moderate rotations) as well as short-term material nonlinearity that incorporates tension, cracking and tension stiffening of the concrete, biaxial compression and compression yielding of the concrete and yielding of the steel. An updated Lagrangian approach is employed to solve the nonlinear finite element stiffness equations. Numerical examples of two reinforced concrete slabs and of a shallow reinforced concrete arch are presented to demonstrate the accuracy and scope of the layered element formulation.     

Computerized modular ratio design of reinforced concrete members subjected to axial load and biaxial bending

A computerized method of analysis and design of reinforced concrete members of arbitrary cross-sections subjected to axial load and biaxial bending is proposed. The design process has been computerized to full automation—in the sense that given the concrete section and the applied loading, the program directly evaluates the amount of reinforcement required and the corresponding stress envelope. The strength of concrete in tension is neglected in the analysis. An iterative process which successively adjusts the section properties according to the stress state is employed. The design process is basically an iterative process of gradually increasing the amount of reinforcement till the permissible stresses are not exceeded. Reinforcement is added at locations of highest mean sequare stress in order to utilize fully the reinforcement added. Multiple loading cases are considered.     

Flexural analysis of reinforced fibrous concrete members using the finite element method

A numerical procedure based on the finite element method is developed for the geometric and material nonlinear analysis of reinforced concrete members containing steel fibres and subjected to monotonic loads. The proposed procedure is capable of tracing the displacements, strains, stresses, crack propagation, and member end actions of these structures up to their ultimate load ranges. A frame element with a composite layer system is used to model the structure. An iterative scheme based on Newton-Raphson's method is employed for the nonlinear solution algorithm. The constitutive models of the nonlinear material behaviour are presented to take into account the nonlinear stress-strain relationships, cracking, crushing of concrete, debonding and pull-out of the steel fibres, and yielding of the reinforcement. The geometric nonlinearity due to the geometrical change of both the structure and its elements are also represented. The numerical solution of a number of reinforced fibrous concrete members are compared with published experimental test results and showed good agreement.     

Prediction of deflection of reinforced concrete shear walls

Reinforced concrete shear walls are used in tall buildings for efficiently resisting lateral loads. Due to the low tensile strength of concrete, reinforced concrete shear walls tend to behave in a nonlinear manner with a significant reduction in stiffness, even under service loads. To accurately assess the lateral deflection of shear walls, the prediction of flexural and shear stiffness of these members after cracking becomes important. In the present study, an iterative analytical procedure which considers the cracking in the reinforced concrete shear walls has been presented. The effect of concrete cracking on the stiffness and deflection of shear walls have also been investigated by the developed computer program based on the iterative procedure. In the program, the variation of the flexural stiffness of a cracked member has been evaluated by ACI and probability-based effective stiffness model. In the analysis, shear deformation which can be large and significant after development of cracks is also taken into account and the variation of shear stiffness in the cracked regions of members has been considered by using effective shear stiffness model available in the literature. Verification of the proposed procedure has been confirmed from series of reinforced concrete shear wall tests available in the literature. Comparison between the analytical and experimental results shows that the proposed analytical procedure can provide an accurate and efficient prediction of both the deflection and flexural stiffness reduction of shear walls with different height to width ratio and vertical load. The results of the analytical procedure also indicate that the percentage of shear deflection in the total deflection increases with decreasing height to width ratio of the shear wall.     

Efficient finite element modelling of reinforced concrete beams retrofitted with fibre reinforced polymers

This paper presents a new simple and efficient two-dimensional frame finite element (FE) able to accurately estimate the load-carrying capacity of reinforced concrete (RC) beams flexurally strengthened with externally bonded fibre reinforced polymer (FRP) strips and plates. The proposed FE, denoted as FRP–FB-beam, considers distributed plasticity with layer-discretization of the cross-sections in the context of a force-based (FB) formulation. The FRP–FB-beam element is able to model collapse due to concrete crushing, reinforcing steel yielding, FRP rupture and FRP debonding.The FRP–FB-beam is used to predict the load-carrying capacity and the applied load-midspan deflection response of RC beams subjected to three- and four-point bending loading. Numerical simulations and experimental measurements are compared based on numerous tests available in the literature and published by different authors. The numerically simulated responses agree remarkably well with the corresponding experimental results. The major features of this frame FE are its simplicity, computational efficiency and weak requirements in terms of FE mesh refinement. These useful features are obtained together with accuracy in the response simulation comparable to more complex, advanced and computationally expensive FEs. Thus, the FRP–FB-beam is suitable for efficient and accurate modelling and analysis of flexural strengthening of RC frame structures with externally bonded FRP sheets/plates and for practical use in design-oriented parametric studies.     

Gradient tree boosting machine learning on predicting the failure modes of the RC panels under impact loads

This paper proposed a new approach in predicting the local damage of reinforced concrete (RC) panels under impact loading using gradient boosting machine learning (GBML), one of the most powerful techniques in machine learning. A number of experimental data on the impact test of RC panels were collected for training and testing of the proposed model. With the lack of test data due to the high cost and complexity of the structural behavior of the panel under impact loading, it was a challenge to predict the failure mode accurately. To overcome this challenge, this study proposed a machine-learning model that uses a robust technique to solve the problem with a minimal amount of resources. Although the accuracy of the prediction result was not as high as expected due to the lack of data and the unbalance experimental output features, this paper provided a new approach that may alternatively replace the conventional method in predicting the failure mode of RC panel under impact loading. This approach is also expected to be widely used for predicting the structural behavior of component and structures under complex and extreme loads.

     

A FEMP method and its application in modeling dynamic response of reinforced concrete subjected to impact loading

The material point method (MPM) takes advantages of both the Eulerian and Lagrangian methods, so it is capable of handling many challenging engineering problems, such as the dynamic responses of reinforced concrete (RC) subjected to blast and impact loadings. However, it is time-consuming to discretize the steel reinforcement bars (“rebars”) in RC by using MPM because the diameter of the steel bar is very small compared with the size of concrete. A hybrid finite element–material point (FEMP) method is proposed, in which the truss element in the traditional finite element method (FEM) is incorporated into the MPM to model the rebars. The proposed FEMP method is implemented in our three-dimensional material point method code, MPM3D®, and validated by several benchmark problems. Finally, it is applied to simulate the dynamic response of RC slab penetrated by projectile, and the numerical results are in good agreement with the experimental data reported in the literature. The proposed idea is applicable to incorporate other types of finite elements into MPM to take advantages of both FEM and MPM.     

Empirical modeling of shear strength of steel fiber reinforced concrete beams by gene expression programming

The addition of steel fibers into concrete improves the postcracking tensile strength of hardened concrete and hence significantly enhances the shear strength of reinforced concrete reinforced concrete beams. However, developing an accurate model for predicting the shear strength of steel fiber reinforced concrete (SFRC) beams is a challenging task as there are several parameters such as the concrete compressive strength, shear span to depth ratio, reinforcement ratio and fiber content that affect the ultimate shear resistance of FRC beams. This paper investigates the feasibility of using gene expression programming (GEP) to create an empirical model for the ultimate shear strength of SFRC beams without stirrups. The model produced by GEP is constructed directly from a set of experimental results available in the literature. The results of training, testing and validation sets of the model are compared with experimental results. All of the results show that GEP model is fairly promising approach for the prediction of shear strength of SFRC beams. The performance of the GEP model is also compared with different proposed formulas available in the literature. It was found that the GEP model provides the most accurate results in calculating the shear strength of SFRC beams among existing shear strength formulas. Parametric studies are also carried out to evaluate the ability of the proposed GEP model to quantitatively account for the effects of shear design parameters on the shear strength of SFRC beams.     

Numerical simulations of oblique penetration into reinforced concrete targets

A dynamic constitutive model based on the tensile and the compressive damage models for concrete was developed and implemented into the three-dimensional finite element code, LS-DYNA. Numerical simulations of oblique penetration into reinforced concrete targets were performed using LS-DYNA. On the basis of the proposed model, the tensile and compressive damages of reinforced concrete after oblique penetration were observed and the deformation of reinforcing steel bars was obtained. Moreover, the depths of penetration for different oblique angles were obtained. The numerical results for the depth of penetration are in good agreement with existing experimental data.     

A fibre model for push-over analysis of underdesigned reinforced concrete frames

Most of the existing reinforced concrete buildings were designed according to early seismic provisions or, sometimes, without applying any seismic provision. Some problems of strength and ductility, like insufficient shear strength, pull-out of rebars, local mechanisms, etc., could characterize their structural behaviour. The above mentioned topics lead to a number of problems in the evaluation of the seismic behaviour of reinforced concrete (RC) frames. Therefore the assessment of existing RC structures requires advanced tools. A refined model and numerical procedure for the non-linear analysis of reinforced concrete frames is presented. The current version of the model proposed is capable of describing the non-linear behaviour of underdesigned reinforced concrete frames including brittle modes of failure. Selected results of an experimental–theoretical comparison are presented to show the capabilities of this model. The results show the capacity of the model of describing both the global behaviour and the local deformation at service and ultimate state.     

Dynamic deformation signatures in reinforced concrete slabs for condition monitoring

We examine the use of ordinary steel and concrete strain gauges to monitor the dynamic response of reinforced concrete (RC) slabs excited in non-destructive vibrational testing. Plots of measured dynamic strains in the embedded steel reinforcement bars and on the concrete surface, as well as of mid-span deflection, are presented at different levels of load-induced damage. The plots show unique strain and deflection signatures that vary with the internal state of the slab, and could be used for condition monitoring and residual strength identification. It is feasible that the techniques outlined could be used in AI-based evaluation tools for RC slabs and other RC structures.     

Prediction of shear strength of FRP-reinforced concrete beams without stirrups based on genetic programming

The use of fibre reinforced polymer (FRP) bars to reinforce concrete structures has received a great deal of attention in recent years due to their excellent corrosion resistance, high tensile strength, and good non-magnetization properties. Due to the relatively low modulus of elasticity of FRP bars, concrete members reinforced longitudinally with FRP bars experience reduced shear strength compared to the shear strength of those reinforced with the same amounts of steel reinforcement. This paper presents a simple yet improved model to calculate the concrete shear strength of FRP-reinforced concrete slender beams (a/d > 2.5) without stirrups based on the gene expression programming (GEP) approach. The model produced by GEP is constructed directly from a set of experimental results available in the literature. The results of training, testing and validation sets of the model are compared with experimental results. All of the results show that GEP is a strong technique for the prediction of the shear capacity of FRP-reinforced concrete beams without stirrups. The performance of the GEP model is also compared to that of four commonly used shear design provisions for FRP-reinforced concrete beams. The proposed model produced by GEP provides the most accurate results in calculating the concrete shear strength of FRP-reinforced concrete beams among existing shear equations provided by current provisions. A parametric study is also carried out to evaluate the ability of the proposed GEP model and current shear design guidelines to quantitatively account for the effects of basic shear design parameters on the shear strength of FRP-reinforced concrete beams.